Описание:The special course is devoted to classical and modern methods of studying nonlinear differential equations and their application to solving urgent problems of the qualitative theory of differential equations. The course assumes an exposition of classical and author's approaches, presents new results obtained in world science, and describes the application of these results in some problems of optimization and control theory. The basis for this course is the special course "Methods of Qualitative Theory of Differential Equations", lectured by the author in Russian, and “Qualitative Theory of Nonlinear Ordinary Differential Equations” lectured by the author in English in Lomonosov Moscow State University which is focused on understanding it by junior students and can be interesting to other students and PhD, using the knowledge gained by students in the field of topology and functional analysis. The special course will help the student and graduate student who is starting serious scientific work to navigate the variety of scientific works of various scientific schools engaged in research in the field of the qualitative theory of nonlinear ordinary equations and their applications to problems of biology, economics, mechanics, and research methods. For each topic, both educational and creative tasks are proposed.